Seminar

Understanding Regressions with Observations Collected at High Frequency over Long Span

Joon Park (Indiana University)

March 3, 2015, 15:30–17:00

Room MS 001

Econometrics and Empirical Economics Seminar

Abstract

In this paper, we consider regressions with observations collected at small time interval over long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this set-up, we show that the standard Wald statistic always diverges to infinity as long as δ → 0 sufficiently fast relative to T → ∞, and regressions become spurious. This is indeed well expected from our asymptotics which shows that, in such a set-up, samples from any continuous time process become strongly dependent with their serial correlation approaching to unity, and regressions become spurious exactly as in the conventional spurious regression. However, as we show in the paper, the spuriousness of Wald test disappears if we account for strong persistency adequately using an appropriate longrun variance estimate. The empirical illustrations in the paper provide a strong and unambiguous support for the practical relevancy of our asymptotic theory.